Abstract:

[EN] In this article we consider the Sobolev orthogonal polynomials associated to the Jacobi's measure on [-1,1] . It is proven that for the class of monic Jacobi-Sobolev orthogonal polynomials, the smallest closed interval that contains its real zeros is $[-\sqrt{1 + 2C}, \sqrt{1 + 2C}]$ with C a constant explicitly determined. The asymptotic distribution of those zeros is studied and also we analyze the asymptotic comparative behavior between the sequence of monic Jacobi-Sobolev orthogonal polynomials and the sequence of monic Jacobi orthogonal polynomials under certain restrictions.